Statistical analysis
For each study, the data will be converted into standardized mean differences (SMDs) as effect size index. The SMD is calculated as the mean difference in telomere length between the SUD (
MSUD) and control (
MControl) groups divided by the pooled standard deviation of the two groups (
S): SMD =
c(
m)(
MSUD –
MControl)/
S, with
c(
m) being a correction factor for small sample sizes defined as
c(
m) = 1 − 3/(4
N – 9),
N being the sum of the two sample sizes [
46]. If means and standard deviations are not reported in the study, formulas will be applied to obtain the SMD from other statistical data (e.g.,
t tests,
F tests,
p values, correlations, odds ratios, etc.) [
47]. Negative SMDs will represent a shorter telomere length for the SUD group compared with the control group. For each SMD, a 95% confidence interval (95% CI) will be calculated. In this meta-analysis, unadjusted effect sizes (SMDs) will be used. The potential influence of confounding factors will be assessed as described below.
Because a high level of heterogeneity is expected, random-effects models will be used a priori for SUD overall and for each independent substance consumed if the number of available studies allows it. Random-effects modeling assumes a genuine diversity in the results of the various studies and incorporates between-studies variance into the calculations. Random-effects models imply to weight each effect size by its inverse variance, this being the sum of the within-study and the between-studies variance. The between-studies variance will be estimated by restricted maximum likelihood [
47]. Average effect size and a 95% CI will then be calculated with the improved method proposed by Hartung and Knapp [
48‐
50]. Instead of assuming a standard normal distribution, the method by Hartung and Knapp assumes a Student
t distribution with
k – 1 degrees of freedom (
k being the number of studies) and an improved estimator of the variance of SMD that takes into account the uncertainty in estimating the between-studies variance. In addition, a 95% prediction interval around the average effect size will be calculated, in order to provide a prediction of the expected true effects if a new study is conducted [
47,
50].
To estimate heterogeneity between studies, the Cochran`s
Q statistic, the
I2 index, and visual inspection of the forest plots will be used.
Q statistic is a weighted sum of the squared of the deviations of individual effect estimates from the overall estimate. A statistically significant result for the
Q statistic is indicative of heterogeneity. The
I2 index is calculated as
I2 = 100(
Q −
df)/
Q, with
df being the degrees of freedom of the
Q statistic:
df =
k – 1 (
k being the number of studies).
I2 is interpreted as the percentage of total variation across studies due to heterogeneity. The
I2 index takes values between 0 and 100% with higher values denoting a greater degree of heterogeneity (0–25%: no or negligible heterogeneity; 25–50%: moderate heterogeneity; 50–75%: large heterogeneity; and 75–100%: extreme heterogeneity).
I2 values of 25% or more will lead to investigate the influence of moderator variables. In addition, heterogeneity will be assessed with the between-studies variance and 95% confidence interval. Finally, following Mathur and VanderWeele’s (2019) proposal, the estimated proportion (and 95% confidence interval) of true effect sizes exceeding a scientifically meaningful threshold will be calculated. In terms of standardized mean difference, we will consider − 0.20 the threshold effect size for these calculations [
51].
In cases of moderate-to-large heterogeneity (
I2 > 25%), we will seek to identify possible explanations using subgroup analyses and meta-regressions based on the most important characteristics of the studies, including items used to evaluate the risk of bias. The analysis of moderating variables will be accomplished by assuming a mixed-effects model. Categorical moderators will be analyzed by comparing the average effect size of each category of the moderator [
52], whereas continuous moderators will be analyzed by means of meta-regressions [
53]. In both cases, the improved
F statistic developed by Knapp and Hartung will be applied for testing the statistical significance of each moderator [
54]. To estimate the proportion of variance accounted for by the moderator, an
R2 index will be calculated [
55].
Research on telomere length for persons with SUD must dedicate special attention to the potential influence of confounding factors. In order to address this point, several sensitivity analyses will be conducted. First, the risk of bias items of the NOS will be analyzed by means of subgroup analyses. Second, the comparability of the groups (cases and controls) is a key issue to assess the potential influence of confounding factors on effect sizes, with age being the most relevant confounding factor. In addition, to apply subgroup analyses to the risk of bias item on comparability of the NOS, simple meta-regressions will also be conducted using the SMDs as a dependent variable and the mean difference in age between cases and controls, the difference in age SDs, the difference in the proportion of males and of Caucasians, and the difference in education levels. Third, another set of subgroup analyses will be conducted with other covariates related to telomere length, such as smoking status, exposure to childhood adversities or other stressful events, and the presence of mental or physical comorbidities.
The presence of publication bias will be examined using the “funnel plot” method using Duval and Tweedie’s trim-and-fill method [
56], the Egger test [
57], and the precision-effect test–precision-effect estimate with standard error (PET-PEESE) method [
58]. A sensitivity analysis will then be performed to assess whether our results were substantially influenced by the presence of any individual study by systematically removing each study and recalculating the significance of the overall results. If conditions impede meta-analysis, data will be narratively presented. All statistical analyses will be conducted using the metafor program in R [
59]. To judge the quality of evidence for all outcomes, the Grading of Recommendations Assessment, Development and Evaluation (GRADE) approach will be used [
60]. Results will be reported according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement [
61].